## Flow of a thin ribbon of molten glass on a bath of molten tin

##### Date

2016

##### Authors

Sangweni, Zinhle Brighty

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##### Abstract

The equations for the
flow of a thin lm of molten glass on a bath of molten
tin are extended to the case in which the viscosity of the molten glass depends
on the temperature. The continuity equation for an incompressible
fluid, the
Navier-Stokes equation and the energy balance equation are written in the
lubrication (thin
fluid lm) approximation. The kinematic boundary condition and the boundary conditions for the normal and tangential stress and
the normal heat
flux are derived on the upper and lower surfaces of the glass
ribbon. It is found for the lubrication approximation that only one equation is
obtained for four unknowns which are the two horizontal velocity components,
the absolute temperature difference and the thickness of the molten glass rib-
bon. The remaining three equations are obtained by taking the calculation
to the next order in the square of the ratio of the thickness to length of the
glass ribbon. The kinematic edge condition and the edge conditions for the
normal and tangential stress and the normal heat
flux are derived. The four
edge conditions and the boundary conditions at the inlet and outlet give the
boundary conditions for the four partial differential equations. It is not the
aim of the dissertation to solve the boundary value problem which has been
derived, either numerically or analytically.

##### Description

A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, for the degree of Master of Science. School of Computer Science and Applied Mathematics. November 7, 2016.

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##### Citation

Sangweni, Zinhle Brighty (2016) Flow of a thin ribbon of molten glass on a bath of molten tin, University of Witwatersrand, Johannesburg, <http://wiredspace.wits.ac.za/handle/10539/21677>